Stochastic bifurcation characteristics of cantilevered piezoelectric energy harvester

Stochastic bifurcation characteristics of cantilevered piezoelectric energy harvester were studied in this paper. Von de Pol differencial item was introduced to interpret the hysteretic phenomena of piezoelectric ceramics, and then the nonlinear dynamic model of piezoelectric cantilever beam subjected to axial stochastic excitation was developed. The stochastic stability of the system was analyzed, and the steady-state probability density function and the joint probability density function of the dynamic response of the system were obtained, and then the conditions of stochastic Hopf bifurcation were analyzed. Numerical simulation shows that stochastic Hopf bifurcation appears when bifurcation parameter varies, which can increase vibration amplitude of cantilever beam system and improve the efficiency of piezoelectric energy harvester. Finally, the theoretical and numerical results were proved by experiments. The results of this paper are helpful to application of cantilevered piezoelectric energy harvester in engineering fields.